Method for processing a signal, in particular a digital audio signal

ABSTRACT

The invention relates to a method for processing a signal, in particular a digital audio signal, suitable for being implemented by a digital signal processor (DSP) having libraries for calculating Fourier transforms from the complex number space to the complex number space, for digitally processing P input signals, P being an integer at least equal to 2, more particularly for filtering said P input signals by the convolution of sampled fast Fourier transforms (FFT), thus obtaining Q output signals, Q being an integer at least equal to 2. According to the invention, the method includes at least the following steps: —grouping said P input signals by twos, one representing the real portion and the other the imaginary portion of a complex number, thus defining one or more input vectors, —filtering said input vector or vectors, passing through the Fourier space, thus generating one or more output vectors, which are complex numbers, the real portion and the imaginary portion of said vector or each one of said output vectors respectively representing one of said Q output signals.

This is a non-provisional application claiming the benefit ofInternational Application Number PCT/FR2009/001342 filed Nov. 25, 2009.

The invention relates to a method for processing a digital audio signalas well as to a digital signal processor programmed for applying themethod.

The invention will find a particular application for digital signalprocessors (DSP) having libraries for calculating Fourier Transformsfrom complex number space to complex number space.

The field of the invention is that of digital audio signal processing.

The calculation of a Fourier Transform of a real signal results incoefficient redundancy. This redundancy is used by certain algorithmsfor limiting the number of calculations and for carrying out thisoperation more rapidly. Such algorithms are notably known from documentsWO-01/33411, US-2002/0083107 or further US-2006/0140291. Certain ofthese algorithms require function libraries with which very fast realcalculations of Fourier Transforms may be performed while optimizing thecalculations according to the hardware capacities of the machines.However, most present DSPs do not have such libraries and only have fastFourier Transforms (FFTs) for complex numbers, i.e. from complex numberspace to complex number space.

The object of the present invention is to propose an alternative to themethods of the state of the art with which true computational burden maybe reduced for filtering operations by convolution of fast FourierTransforms.

Another object of the invention is to propose such a method,particularly suitable for DSPs having libraries for FFT calculationsfrom complex number space to complex number space.

Other objects and advantages of the present invention will becomeapparent during the description which follows, which is only given as anindication and does not have the purpose of limiting it.

The invention first of all relates to a method for processing a digitalaudio signal, in order to achieve spatialization of sound, said methodbeing applied by a digital signal processor (DSP) having libraries forcalculating Fourier Transforms from complex number space to complexnumber space, for digital processing of P input signals, P being aninteger greater than or equal to 2, for filtering said P input signalsby the convolution of sampled Fast Fourier Transforms (FFTs), therebyobtaining Q output signals, Q being an integer greater than or equal totwo.

According to the invention, the method comprises at least the followingsteps:

grouping said P input signals by twos, one representing the realportion, the other the imaginary portion of a complex number, therebydefining one or more input vectors,

carrying out the filtering on said input vector(s) by passing throughFourier space, thereby generating one or more complex output vectors,the real portion and the imaginary portion of said or each of saidoutput vectors respectively representing one of said Q output signals.

The invention will be better understood upon reading the followingdescription accompanied by the appended figures wherein:

FIG. 1 is a schematic diagram illustrating filtering by the convolutionof Fast Fourier Transforms of an input signal in order to obtain anoutput signal, according a non-optimized algorithm of the state of theart (case of one input, one output),

FIG. 2 illustrates filtering by the convolution of Fast FourierTransforms of an input signal in order to obtain two output signalsaccording to a non-optimized algorithm of the state of the art (case ofone input, two outputs),

FIG. 3 is a schematic diagram illustrating filtering by the convolutionof Fast Fourier Transforms of two input signals in order to obtain twooutput signals according to a non-optimized algorithm of the state ofthe art (case of two inputs, two outputs),

FIG. 4 is a schematic diagram illustrating the processing methodaccording to the invention, for the filtering of two input signals inorder to obtain two output signals (P=2, Q=2),

FIG. 5 is a schematic diagram illustrating the generalization of themethod according to the invention as illustrated in FIG. 4 for filteringa number of signals P strictly greater than 2, an integer such thatP=2×L with L an integer (P=2L, Q=2),

FIG. 6 is a schematic diagram illustrating the generalization of themethod according to the invention as illustrated in FIG. 5 wherein P isgreater than or equal to 2, an even integer such that P=2L with L aninteger and Q strictly greater than 2, an even integer such that Q=2Mwith M an integer (P=2L, Q=2M).

First of all, we begin by describing filtering by convolution of FourierTransforms, which is not optimized, according to the state of the art,more particularly the following cases:

a) an input signal towards one output,

b) an input signal towards two outputs,

c) two input signals towards two output signals (spatialization of twosources on a stereo output).

Case a): one input signal→one output signal (digital filtering)

This case is illustrated in the diagram of FIG. 1.

Let e(t) be a signal which is desirably to be convolved with a signala(t).

a(t) is the impulse response to be applied

let the filter be A(f)=FFT[(a(t))]

let E(f)=FFT [e(t)]

We therefore have the resulting signal from the outputs:s(t)=e(t)

a(t)=IFFT[E(f)·A(f)]=IFFT[FFT(e(t))·FFT(a(t))]

Wherein FFT is the Fast Fourier Transform and IFFT is the inverse FastFourier Transform.

This filtering may be used on a window of size N. By using standardoverlap-add or overlap-save techniques, e(t) may be replaced withe(t)_(N) corresponding to the samples taken on the window of size N andFFT with FFT_(N) which is the Fast Fourier Transform on N samples.

The computing time depends for this type of operation essentially on thenumber of FFTs or IFFTs to be computed.

By taking the FFT as a time unit, and by assuming as a simplifyingassumption that the computing time of an FFT is equivalent to that of anIFFT, the computing time is 3 FFT.

Case b): 1 input signal→two output signals (example: spatialization of asource on a stereo output).

This case is illustrated in the diagram of FIG. 2.

Let us define the following filters:

-   -   a direct filter a(t),    -   an indirect filter (b(t),

The output signals are therefore s₁ and s₂ such that:S ₁(f)=FFT[s ₁(t)]=E(f)·A(f)S ₂(f)=FFT[s ₂(t)]=E(f)·B(f)

By taking FFT as a time unit, the computing time is 5 FFT.

Case c): two input signals→two output signals (application example:specialization of two sources on a stereo output)

This case is illustrated in the diagram of FIG. 3.

Let e₁ be an input signal and e₂ an input signal.

Let us define the following filters a, b, d, c, such that:

$\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} = {\begin{pmatrix}{a(t)} & {d(t)} \\{b(t)} & {c(t)}\end{pmatrix} \otimes \begin{pmatrix}e_{1} \\e_{2}\end{pmatrix}}$

The output signals are therefore s₁ and s₂ such that:S ₁(t)=IFFT[A(f)·E ₁(f)]+IFFT[D(f)·E ₂(f)].S ₂(t)=IFFT[B(f)·E ₁(f)]+IFFT[C(f)·E ₂(f)].

By taking FFT as a time unit, the computing time is here 10 FFT.

Certain digital signal processors which we call a DSP for “DigitalSignal Processor” may have a large amount of memory on board. Thefilters A(f), B(f), D(f), C(f) may then be stored in phase space(further called Fourier space or frequency space), which takes up twiceas much memory on the DSP than if they were stored in time space, i.e.in their form a(t), b(t), d(t), c (t). Thus 4 FFT are saved. Thecomputing time may then be reduced to 6 FFT.

The invention relates to a method for processing a digital audio signalin order to produce spatialization of sound, said method being appliedby a digital signal processor (DSP) having libraries for calculatingFourier transforms from complex number space to complex number space,for digital processing of P input signals, P being an integer greater orequal to 2, for the filtering of said P input signals by the convolutionof sampled fast Fourier transforms (FFT), thereby obtaining Q outputsignals, Q being an integer greater than or equal to 2.

According to the invention, the method comprises at least the followingsteps:

-   -   grouping said P input signals by twos, one representing the real        portion, the other one the imaginary portion of a complex        number, thereby defining one or several input vectors,    -   performing filtering on said input vector(s) by passing through        Fourier space, thereby generating one or more complex output        vectors, the real portion and the imaginary portion of said or        of each of said output vectors respectively representing one of        said Q output signals.

Said or each of said output vectors may be obtained in the followingway:

(1) a filtering operator is applied on said input vector, in the casewhen P=2, thereby giving a result or if necessary, according to anotheralternative, in the case when P>2, on each of said input vectors,thereby giving several intermediate results,

(2) in the case when P>2, said intermediate results obtained in theprevious step are summed in Fourier space.

(3) the result of step (1) or (2) is subject to an output vector.

Various embodiments of the invention will be described subsequently, andmore particularly the following cases:

1) two input signals→2 output signals (P=2, Q=2),

2) 2.L input signals→2 output signals (P=2.L, Q=2),

3) 2.L input signals→2.M output signals (P=2.L, Q=2.M),

4) 2.L+1 input signals→2.M+1 output signals (P=2.L+1, Q=2.M+1).

L and M are non-zero natural integers greater than or equal to 1.

The method thus consists of grouping the input signals by twos, onerepresenting the real portion, the other one the imaginary portion of aninput vector. Once it is in phase space, the input vector undergoesprocessing by a basic block referenced as 1.

With the method it is possible to considerably reduce the computing timeas compared with non-optimized standard methods. The table belowcompares in FFT time units, the computing times between the methodaccording to the invention and the non-optimized standard processing,and this for the different embodiments which will be developedsubsequently.

For example, for spatialization of 64 input signals on quadraphony (L=32and M=2), the method allows a reduction in the number of FFTs from 320to 34.

Engine Standard according to the processing invention and Case/computingand storage storage of the time (in number Standard of the filtersfilters in of FFTs) processing in phase space phase space 1) P = 2, Q =2 10 6 2 2) P = 2.L, Q = 2 10.L 6.L L + 1 3) P = 2.L, 8.L.M 4.L.M + 2.LL + M Q = 2.M 4) P = 2.L + 1, 8.L.M + 6.L + 8.L.M + 4.L + L + M + 2 Q =2.M + 1 4.M + 3 2.M + 2We shall now develop the various aforementioned embodiments:Case 1): 2 input signals→2 output signals (P=2, Q=2):This case is illustrated in the diagram of FIG. 4.The following variables are defined:e₁(t) and e₂(t) are said P input signals,s₁(t) and s₂(t) are said Q output signals.a(t), b(t), c(t) and d(t) are filters defined such that:

$\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} = {\begin{pmatrix}{a(t)} & {d(t)} \\{b(t)} & {c(t)}\end{pmatrix} \otimes \begin{pmatrix}e_{1} \\e_{2}\end{pmatrix}}$wherein

is the convolution operator.e0(t) is said input vector such that e0(t)=e₁(t)+j·e₂(t),s0(t) is said output vector such that s0(t)=s₁(t)+j·s₂(t).Said filtering operator further called “basic block” referenced as 1 inFIG. 4 is such that:

$S = {{\frac{F + H}{2} \cdot E} + {{\frac{F - H}{2} \cdot \overset{\sim}{E}}*}}$wherein:* is the conjugate complex operator such that (x+j·y)*=x−j·y,˜ is the operator for inverting indices such that {tilde over(E)}(i)=E(N−i) and {tilde over (E)}(0)=E(0) andE(f)=FFT(e0(t)),S(f)=FFT(s0(t)),F(f)=FFT[a(t)+j·b(t)],H(f)=FFT[c(t)−j·d(t)],

The filtering diagram is illustrated in FIG. 4. By the invention, themethod only requires 3 FFTs and one IFFT, or only one FFT and one IFFTif the filters

$\frac{\left( {F + H} \right)}{2}\mspace{14mu}{and}\mspace{14mu}\frac{\left( {F - H} \right)}{2}$are stored in phase space. The computing time is therefore equivalent to2 FFTs.Case 2): 2.L input signals→2 output signals (P=2.L, Q=2)This embodiment is particularly illustrated in FIGS. 4 and 5.P>2, an even integer such that P=2L, with L an integer, Q=2,

The following variables are defined:

e₁(t), . . . , e_(2k−1)(t), e_(2k)(t), . . . , e_(2L)(t), are said Pinput signals,

s₁(t), s₂(t) are said Q output signals.

{a_(k)(t), b_(k)(t), c_(k)(t), d_(k)(t)} is the set of filters definedsuch that kε[1 to L] and:

$\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} = {\sum\limits_{k = 1}^{L}{\begin{pmatrix}{a_{k}(t)} & {d_{k}(t)} \\{b_{k}(t)} & {c_{k}(t)}\end{pmatrix} \otimes \begin{pmatrix}{e_{{2k} - 1}(t)} \\{e_{2k}(t)}\end{pmatrix}}}$wherein

is the convolution operator.{e0_(k)(t)}, such that kε[1 to L] ande0_(k)(t)=e_(2k−1)(t)+j·e_(2k)(t), is the set of input vectors,s0(t) is said output vector such thats0(t)=s₁(t)+j·s₂(t).

Said filtering operator associated with said source vector e0_(k)(t) issuch that:

$S_{k} = {{\frac{F_{k} + H_{k}}{2} \cdot E_{k}} + {{\frac{F - H}{2} \cdot {\overset{\sim}{E}}_{k}}*}}$

wherein:

-   -   * is the conjugate complex operator,    -   ˜ is the operator for inverting indices as defined earlier,        and

${{E_{k}(f)} = {F\; F\;{T\left( {e\; 0_{k}(t)} \right)}}},{{\sum\limits_{k = 1}^{L}{S_{k}(f)}} = {F\; F\;{T\left( {s\; 0(t)} \right)}}},{{F_{k}(f)} = {F\; F\;{T\left\lbrack {{a_{k}(t)} + {j \cdot {b_{k}(t)}}} \right\rbrack}}},{{H_{k}(f)} = {F\; F\;{T\left\lbrack {{c_{k}(t)} - {j \cdot {d_{k}(t)}}} \right\rbrack}}}$

By using the basic block referenced as 1, it is possible to save onIFFTs by summing the s_(k) in Fourier space (phase space). Once thesummation is achieved, it is possible with a single IFFT to obtain theresult s1 and s2 (FIG. 5).

Finally with this method, only L FFTs and 1 IFFT are required. Thecomputing time is equivalent to L+1 FFTs.

Case 3): 2L input signals→2.M output signals (P=2.L, Q=2.M):

This case is illustrated in FIGS. 4, 5 and 6. P≧2, an even integer suchthat P=2L, with L an integer. Q>2, an even integer such that Q=2M, withM an integer. P may be strictly greater than 2.

The following variables are defined:

e₁(t), . . . , e_(2k−1)(t), e_(2k)(t), . . . , e_(2L)(t), are said Pinput signals,

s₁(t), . . . , s_(2m−1)(t), s_(2m)(t), . . . , s_(2M)(t), are said Qoutput signals.

{a_(m,k)(t), b_(m,k)(t), c_(m,k)(t), d_(m,k)(t)} is the set of filtersdefined such that mε[1 to M] and kε[1 to L] and

$\begin{pmatrix}{s_{{2m} - 1}(t)} \\{s_{2m}(t)}\end{pmatrix} = {\sum\limits_{k = 1}^{L}{\begin{pmatrix}{a_{m,k}(t)} & {d_{m,k}(t)} \\{b_{m,k}(t)} & {c_{m,k}(t)}\end{pmatrix} \otimes \begin{pmatrix}{e_{{2k} - 1}(t)} \\{e_{2k}(t)}\end{pmatrix}}}$wherein

is the convolution operator,{e0_(k)(t)}, such that kε[1 to L] ande0_(k)(t)=e_(2k−1)(t)+j·e_(2k)(t), is the set of input vectors,{s0_(m)(t)}, such that mε[1 to M] ands0_(m)(t)=s_(2m−1)(t)+j·s_(2m)(t), is the set of output vectors. Saidfiltering operator associated with said source vector e0_(k)(t) and withsaid output vector s0_(m)(t) is such that:

$S_{m,k} = {{\frac{F_{m,k} + H_{m,k}}{2} \cdot E_{k}} + {{\frac{F_{m,k} - H_{m,k}}{2} \cdot {\overset{\sim}{E}}_{k}}*}}$wherein:* is the conjugate complex operator,˜ is the operator for inverting indices as defined earlier,and

${{E_{k}(f)} = {F\; F\;{T\left( {e\; 0_{k}(t)} \right)}}},{{\sum\limits_{k = 1}^{L}{S_{m,k}(f)}} = {F\; F\;{T\left( {s\; 0_{m}(t)} \right)}}},{{F_{m,k}(f)} = {F\; F\;{T\left\lbrack {{a_{m,k}(t)} + {j \cdot {b_{m,k}(t)}}} \right\rbrack}}},{{H_{m,k}(f)} = {F\; F\;{T\left\lbrack {{c_{m,k}(t)} - {j \cdot {d_{m,k}(t)}}} \right\rbrack}}}$

This method amounts to applying M times the method applied in case 2, asillustrated in FIG. 6.

By using the basic block referenced as 1, this method requires L FFTsfor each E_(k) and M IFFTs for each S0_(k) in the case when the filtersare recorded in frequency form. The computing time is thereforeequivalent to (L+M)FFTs.

Case 4: 2.L+1 signals→2.M+1 output signals (P=2.L+1, Q=2.M+1).

This case is processed by the method seen in case 3) by adding a zeroinput signal and a zero output signal. The computing time is thereforeequivalent to L+M+2.

The generalization, P input signals, Q output signals, consists ofreducing P and Q to the greater or equal even integer by adding a zeroinput signal and/or a zero output signal, depending on the case. Forexample, when P is an odd integer, a zero input signal is added so as toapply the method of case 2 or 3 on an even number of input signals.Also, when Q is an odd integer, a zero output signal is added so as toapply the method of case 3 on an even number of output signals.

Of course, the method is applied on sampled and windowed signals. These“overlap-save” or “overlap-add” methods known per se may be applied inorder to avoid artefacts on the windowings. Cross-fade methods may beapplied in order to avoid the artefacts upon changing a filter.

The invention will also relate to a digital signal processor (DSP)notably having libraries for calculating Fourier transforms from complexnumber space to complex number space and programmed for applying themethod according to the invention.

Naturally, other embodiments might have been envisioned by the personskilled in the art without however departing from the scope of theinvention as defined by the claims hereafter.

The invention claimed is:
 1. A method for processing a digital audiosignal for achieving spatialization of sound, said method being appliedby a digital signal processor (DSP) having libraries for calculatingFourier transforms from complex number space to complex number space,for digital processing of P input signals, P being an integer equal to2, for filtering said P input signals by the convolution of sampled fastFourier transforms (FFT), thereby obtaining Q output signals, Q being aninteger equal to 2, wherein the method comprises at least the followingsteps: grouping said P input signals, one representing the real part,the other the imaginary part of a complex number, thereby defining atleast one input vector, achieving filtering on said at least one inputvector by passing through a Fourier space, thereby generating at leastone complex output vector, the real portion and the imaginary portion ofsaid at least one output vector representing one of said Q outputsignals respectively, and wherein said at least one output vector isobtained in the following way: a filtering operator is applied on saidinput vector thereby giving a result, the result is subject to aninverse fast Fourier transform, thereby obtaining said at least oneoutput vector, and wherein: e₁(t) and e₂(t) are said input P inputsignals, s₁(t) and s₂(t) are said Q output signals, a(t), b(t), c(t) andd(t) are filters defined such that: $\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} = {\begin{pmatrix}{a(t)} & {d(t)} \\{b(t)} & {c(t)}\end{pmatrix} \otimes \begin{pmatrix}{e_{1}(t)} \\{e_{2}(t)}\end{pmatrix}}$ wherein

is the convolution operator, e0(t) is said input vector such thate0(t)=e ₁(t)+j·e ₂(t), s0(t) is said output vector such thats0(t)=s₁(t)+j·s₂(t), said filtering operator is such that:$S = {{\frac{F + H}{2} \cdot E} + {{\frac{F - H}{2} \cdot \overset{\sim}{E}}*}}$wherein: * is the conjugate complex operator, ˜ is the operator forinverting indices and E(f)=FFT(e0(t)), S(f)=FFT(s0(t)),F(f)=FFT[a(t)+j·b(t)], H(f)=FFT[c(t)−j·d(t)], wherein FFT designates thefast Fourier transform operator.
 2. A method for processing a digitalaudio signal for achieving spatialization of sound, said method beingapplied by a digital signal processor (DSP) having libraries forcalculating Fourier transforms from complex number space to complexnumber space, for digital processing of P input signals, P being aninteger greater than 2, for filtering said P input signals by theconvolution of sampled fast Fourier transforms (FFT), thereby obtainingQ output signals, Q being an integer equal to 2, wherein the methodcomprises at least the following steps: grouping said P input signals bytwos, one representing the real part, the other the imaginary part of acomplex number, thereby defining at least one input vector, achievingfiltering on said at least one input vector by passing through a Fourierspace, thereby generating at least one complex output vector, the realportion and the imaginary portion of said at least output vectorrepresenting one of said Q output signals respectively, and wherein saidat least one output vector is obtained in the following way: a filteringoperator is applied on each of said at least one input vectors, therebygiving several intermediate results, said intermediate results obtainedby said filtering are summed in the Fourier space, the result of thesumming of said intermediate results is subject to an inverse fastFourier transform, thereby obtaining said output vector, and wherein:P>2, an even integer such that P=2L, with L an integer, Q=2, e₁(t), . .. , e_(2k−1)(t), e_(2k)(t), . . . , e_(2L)(t), are said P input signals,s₁(t), s₂(t) are said Q output signals, {a_(k)(t), b_(k)(t), c_(k)(t),d_(k)(t)} is the set of filters defined such that kε[1 to L] and:$\begin{pmatrix}{s_{1}(t)} \\{s_{2}(t)}\end{pmatrix} = {\sum\limits_{k = 1}^{L}{\begin{pmatrix}{a_{k}(t)} & {d_{k}(t)} \\{b_{k}(t)} & {c_{k}(t)}\end{pmatrix} \otimes \begin{pmatrix}{e_{{2k} - 1}(t)} \\{e_{2k}(t)}\end{pmatrix}}}$ wherein

is the convolution operator, {e0_(k)(t)}, such that kε[1 to L] ande0_(k)(t)=e_(2k−1)(t)+j·e₂k(t), is the set of input vectors, s0(t) issaid output vector such that s0(t)=s₁(t)+j·s₂(t), said filteringoperator associated with said source vector e0_(k)(t) is such that:$S_{k} = {{\frac{F_{k} + H_{k}}{2} \cdot E_{k}} + {{\frac{F - H}{2} \cdot {\overset{\sim}{E}}_{k}}*}}$wherein: * is the conjugate complex operator, ˜ is the operator forinverting indices, and${{E_{k}(f)} = {F\; F\;{T\left( {e\; 0_{k}(t)} \right)}}},{{\sum\limits_{k = 1}^{L}{S_{k}(f)}} = {F\; F\;{T\left( {s\; 0(t)} \right)}}},{{F_{k}(f)} = {F\; F\;{T\left\lbrack {{a_{k}(t)} + {j \cdot {b_{k}(t)}}} \right\rbrack}}},{{H_{k}(f)} = {F\; F\;{T\left\lbrack {{c_{k}(t)} - {j \cdot {d_{k}(t)}}} \right\rbrack}}}$wherein FFT designates the fast Fourier transform operator.
 3. Themethod according to claim 2, wherein, when the number of input signalsis an uneven integer, a zero input signal is added so as to apply themethod of claim 2 on an even number of input signals.
 4. A method forprocessing a digital audio signal for achieving spatialization of sound,said method being applied by a digital signal processor (DSP) havinglibraries for calculating Fourier transforms from complex number spaceto complex number space, for digital processing of P input signals, Pbeing an integer greater than or equal to 2, for filtering said P inputsignals by the convolution of sampled fast Fourier transforms (FFT),thereby obtaining Q output signals, Q being an integer greater than 2,wherein the method comprises at least the following steps: grouping saidP input signals by twos, one representing the real part, the other theimaginary part of a complex number, thereby defining at least one inputvector, achieving filtering on said at least one input vector by passingthrough a Fourier space, thereby generating at least one complex outputvector, the real portion and the imaginary portion of said at least oneoutput vector representing one of said Q output signals respectively,and wherein said at least one output vector is obtained in the followingway: a filtering operator is applied on each of said at least one inputvector, thereby giving several intermediate results, said intermediateresults obtained by said filtering are summed in Fourier space, theresult of the summing of the intermediate results is subject to aninverse fast Fourier transform, thereby obtaining said at least oneoutput vector, and wherein: P≧2 an even integer such that P=2L, with Lan integer, Q>2, an even integer such that Q=2M, with M an integer,e₁(t), . . . e_(2k−1)(t), e_(2k)(t), . . . e_(2L)(t), are said P inputsignals, s₁(t), . . . s_(2m−1)(t), s_(2m)(t), . . . s_(2M)(t), are saidQ output signals, {a_(m,k)(t), b_(m,k)(t), c_(m,k)(t), d_(m,k)(t)} isthe set of filters defined such as mε[1 to M] and kε[1 to L] and$\begin{pmatrix}{s_{{2m} - 1}(t)} \\{s_{2m}(t)}\end{pmatrix} = {\sum\limits_{k = 1}^{L}{\begin{pmatrix}{a_{m,k}(t)} & {d_{m,k}(t)} \\{b_{m,k}(t)} & {c_{m,k}(t)}\end{pmatrix} \otimes \begin{pmatrix}{e_{{2k} - 1}(t)} \\{e_{2k}(t)}\end{pmatrix}}}$ wherein

is the convolution operator, {e0_(k)(t)}, such that kε[1 to L] ande0_(k)(t)=e_(2k−1)(t)+j·e_(2k)(t), is the set of input vectors,{s0_(m)(t)}, such that mε[1 to M] and s0_(m)(t)=s_(2m−1)(t)+j·s_(2m)(t),is the set of output vectors, said filtering operator associated withsaid source vector e0_(k)(t) and with said at least one output vectors0_(m)(t) is such that:$S_{m,k} = {{\frac{F_{m,k} + H_{m,k}}{2} \cdot E_{k}} + {{\frac{F_{m,k} - H_{m,k}}{2} \cdot {\overset{\sim}{E}}_{k}}*}}$wherein: * is the conjugate complex operator, ˜ is the operator forinverting indices, and${{E_{k}(f)} = {F\; F\;{T\left( {e\; 0_{k}(t)} \right)}}},{{\sum\limits_{k = 1}^{L}{S_{m,k}(f)}} = {F\; F\;{T\left( {s\; 0_{m}(t)} \right)}}},{{F_{m,k}(f)} = {F\; F\;{T\left\lbrack {{a_{m,k}(t)} + {j \cdot {b_{m,k}(t)}}} \right\rbrack}}},{{H_{m,k}(f)} = {F\; F\;{T\left\lbrack {{c_{m,k}(t)} - {j \cdot {d_{m,k}(t)}}} \right\rbrack}}},$wherein FFT designates the fast Fourier transform operator.
 5. Themethod according to claim 4, wherein, when the number of output signalsis an uneven integer, a zero output signal is added so as to apply themethod of claim 4 on an even number of output signals.
 6. The methodaccording to any one of claims 1, 2 or 4, wherein the method is appliedon sampled and windowed signals, by applying “overlap-save” or“overlap-add” in order to avoid artefacts on windowings.
 7. The methodaccording to claim 1, claim 2, or claim 4, wherein cross-fade methodsare applied for avoiding artefacts upon changing filter.
 8. A digitalsignal processor (DSP) having libraries for calculating Fouriertransforms from complex number space to complex number space, andprogrammed for applying a method for digital processing of P inputsignals, P being an integer greater than or equal to 2, for filteringsaid P input signals by the convolution of sampled fast Fouriertransforms (FFT), thereby obtaining Q output signals, Q being an integergreater than or equal to 2, wherein the method comprises at least thefollowing steps: grouping said P input signals by twos, one representingthe real part, the other the imaginary part of a complex number, therebydefining at least one input vector, achieving filtering on said at leastone input vector by passing through a Fourier space, thereby generatingat least one complex output vector, the real portion and the imaginaryportion of said or each of said at least one output vector representingone of said Q output signals respectively, and wherein said at least oneoutput vector is obtained in the following way: (1) a filtering operatoris applied on said input vector, in the case when P=2 thereby giving aresult or if necessary, according to another alternative, in the casewhen P>2, on each of said input vectors, thereby giving severalintermediate results, (2) in the case when P>2, said intermediateresults obtained by said filtering are summed in the Fourier space, (3)the result of step (1) or (2) is subject to an inverse fast Fouriertransform, thereby obtaining said output vector.